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Консультация № 187000
19.12.2012, 23:16
78.80 руб.
20.12.2012, 17:10
0
2
2
Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
Даны законы распределения двух независимых случайных величин:
Найти постоянную величину С, математическое ожидание и дисперсию случайной величины
.
Даны законы распределения двух независимых случайных величин:
Найти постоянную величину С, математическое ожидание и дисперсию случайной величины
.
Обсуждение
20.12.2012, 01:10
общий
это ответ
Здравствуйте, roover!
Найдём С из условия
Случайная величина Х имеет равномерное распределение
f(x)=1/36 при х[$8712$][-18, 18]; f(x)=0 при х[$8713$][-18, 18].
Её математическое ожидание M(X)=(a+b)/2=(-18+18)/2=0, дисперсия D(X)=((b-a)2)/12=((18-(-18))^2)/12=108.
Случайная величина Y имеет показательное распределение
f(у)=9е-9у при у>0; f(y)=0 при y[$8804$]0.
Параметр этого распределения [$955$]=9.
Математическое ожидание M(Y)=1/[$955$]=1/9, дисперсия D(Y)=1/[$955$]=1/9.
Используя свойства математического ожидания и дисперсии, находим:
M(Z)=M(X/36-54Y)=M(X)/36-54M(Y)=0/36-54[$183$](1/9)=-6.
D(Z)=D(X/36-54Y)=(1/36)2D(X)+542D(Y)=108/1296+2916/81=1/12+36=433/12.
Найдём С из условия
Случайная величина Х имеет равномерное распределение
f(x)=1/36 при х[$8712$][-18, 18]; f(x)=0 при х[$8713$][-18, 18].
Её математическое ожидание M(X)=(a+b)/2=(-18+18)/2=0, дисперсия D(X)=((b-a)2)/12=((18-(-18))^2)/12=108.
Случайная величина Y имеет показательное распределение
f(у)=9е-9у при у>0; f(y)=0 при y[$8804$]0.
Параметр этого распределения [$955$]=9.
Математическое ожидание M(Y)=1/[$955$]=1/9, дисперсия D(Y)=1/[$955$]=1/9.
Используя свойства математического ожидания и дисперсии, находим:
M(Z)=M(X/36-54Y)=M(X)/36-54M(Y)=0/36-54[$183$](1/9)=-6.
D(Z)=D(X/36-54Y)=(1/36)2D(X)+542D(Y)=108/1296+2916/81=1/12+36=433/12.
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